A21. 2d propagation, stationary, spherical coordinates

The purpose of this test is to verify the correct implementation of spherical coordinates, both for the first and the second order scheme.

A domain with deep water is considered . The domain extends from longitude -40° to 140°, and from latitude -60° to +60°.

At the Southern boundary an incident wave field is assumed which propagates in N direction. This incident wave field has a Jonswap spectrum with narrow directional distribution. The peak period is 20 s.

This is a case of pure propagation, so all source terms in the action balance equation are switched off.

According to theory the wave direction should be N in the whole domain; the wave height should be dependent only on latitude. The wave energy should be proportional to 1/cos(y), where y is latitude. Hs consequently is proportional to 1/sqrt(cos(y)).

The distribution of Hs over space (in the form of isolines) together with the average directions is shown for: a, the BSBT scheme, b, the SORDUP scheme.

The values computed for the central meridian are shown together with the analytical solution.

2 cases are considered:

A21a
1st order BSBT scheme
A21b
2nd order upwind scheme

© 2012: Nico Booij